Make a list of all the homework problems you were given. Pick one problem at
random from each section and give it a whack. If it whacks you back, you need
to review that section. If you breeze through this, the exam is in the bag. It
is almost always true that if you have mastered the assigned homework problems
you will do well on the exam.

It is far easier for an instructor to reuse an old exam then to cook up a new
one. Exam questions are really hard for a professor to make up. Questions
must be not too easy but not impossible (although this latter restriction is
sometimes inadvertently overlooked). All the numbers have to work out nicely.
So the instructor will very likely leaf through the previous couple of years'
exams and modify some problems slightly. Not more than two years because the
older exams are hopelessly lost under piles of papers.

An opportunity for the enterprising student!

3.

Seek professional counseling.

What if you don't know how to do a problem, and you can't make heads or tails
out of the convoluted explanation in your text book, and it's not one of the
subjects covered in this trusty book? What then?

It's time for the pros to earn their keep. Seek out your professor or teaching
assistant for help. Unfortunately at such times they tend to be either:

(a)

In bed sleeping, since it's 3 A.M.

(b)

In their offices surrounded by 247 other students who have finally
realized that the professor's promise that ``eventually, this will
all become clear" was a substantial misrepresentation of the truth.

(c)

Hiding out somewhere. Nowhere to be found.

So what to do? Panic perhaps?

No, no, no. You have not yet used the really valuable resource. Your fellow
students.

4.

Seek amateur counseling.

Students who have mastered a topic like integration by parts achieve no greater
joy than when explaining it to their unenlightened peers. You can vastly
increase the collective happiness and self-esteem on your campus by finding the
student who was paying attention the day you slept late and getting them to
explain the idea to you. A student who took the course last year might also do
the trick, though chances are good that much of what they remember is wrong.
Anyway, student explanations are much less likely to involve phrases like ``by
completeness and compactness of the unit interval" or ``using the third Peano
axiom" or something like that.

5.

Practice under exam conditions.

It's easy to think you understand the
material better than you really do. You can fool yourself into thinking
you can solve a problem when you are looking at the answer book or at a
worked out solution. When the exam comes around, your mind is a blank
without the example to follow. Test your knowledge of a topic by trying problems
under exam conditions. Pick out one problem from each of the types that are to
be covered on the exam. Give yourself one hour to do your ersatz exam and see
how it goes. If you can do it under those conditions, the exam should be a
cinch.